Conventionally, a kid bicycle is provided with two auxiliary wheels that are separately connected to two ends of a rear wheel hub of the kid bicycle via two L-shaped bars, so as to provide the kid bicycle with increased balance for a small child to ride it safely without the risk of becoming tilted over. The auxiliary wheels give the kid bicycle extra support and protection, helping a small child to transit from a kid tricycle to the kid bicycle. However, when the child grows up and the auxiliary wheels are no longer needed, the auxiliary wheels fixedly connected to two lateral sides of the rear wheel via the L-shaped bars tend to touch and rub the ground surface whenever the child riding the bicycle makes a turn. In some undesirable conditions, the auxiliary wheels rubbing the ground surface would even cause tilting over of the bicycle. There are developed some auxiliary wheel folding mechanisms, and patent applications have been filed for them. A most common type of such auxiliary wheel folding mechanisms includes an elastic clamping plate provided in a hollow tubular axle of the auxiliary wheel. When the auxiliary wheel axle is turned to a predetermined angular position, the elastic clamping plate will extend into the hollow space in the axle and thereby holds the axle to that angular position. In another design, a torsional spring is used to turn the auxiliary wheel axle to a predetermined angle of inclination. Unlike the prior art, the present invention provides an auxiliary wheel structure to enable more convenient adjusting of the auxiliary wheels on a kid bicycle to a folded position.